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APPLICATION OF THE UEC / UEP CODES
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Figure 10.25 Influence of errors in data compressed by LZ77 coding. Source: [FUJI03]. 2003 IEICE Japan.
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these three elements. Errors in the matched length corrupt the shift operations of the buffer and affect the decoding of the following words. Errors in the offset and the last symbol corrupt the decoding only of the corresponding word; only the strings that depend on the erroneous words are decompressed incorrectly. So errors in the matched length cause more serious damage to the decompression than those in the offset and the last symbol. This result is veri ed by computer simulation. Figure 10.25 shows the relation between the error location in the compressed data and the in uence of the error to the decompressed data. The source le is paper1, and the in uence of the error is evaluated in the same manner as in Figure 10.23. The lengths of the offset, the matched length, and the last symbol in the compressed data are 12, 4, and 8 bits, respectively. In the three cases, 4-bit burst errors are injected in the offset, the matched length, and the last symbol of the compressed data. This says that errors in the matched length give more serious damage to the decompression than those in the offset and the last symbol. Also errors in the former part of the matched length corrupt larger amounts of compressed data than those in the latter part. Therefore the matched length in the compressed words, especially its former part of the compressed data, should be strongly protected from errors. Encoding Method The encoding scheme divides the compressed data into three sets. The rst set consists of the offsets and the last symbols. The second and the third sets are the former and latter halves of the collected matched lengths, respectively. These three sets are encoded by error control codes separately. Since errors in the second set give more
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CODES FOR UNEQUAL ERROR CONTROL / PROTECTION (UEC / UEP)
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Figure 10.26 Encoding process in LZ77 coding. Source: [FUJI03]. 2003 IEICE Japan.
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serious damage to the decompressed data, the code in this set has stronger error control capability than the codes in the other sets. The following shows the encoding method, which is illustrated in Figure 10.26. Step 1. Compress by LZ77 coding, and let the compressed data be C1;1 C1;2 C1;3 C2;1 C2;2 C2;3 CN;1 CN;2 CN;3 , where Ci;1 , Ci;2 , and Ci;3 are the offset of the matched string in the lookahead buffer, the matched length, and the last symbol of the parsed string, respectively, in the i-th word for 1 i N. Step 2. Divide the compressed data into three sets. The rst set consists of the offsets and the last symbols, C1;1 C1;3 C2;1 C2;3 CN;1 CN;3 . The second and the third sets are the former and the latter half of the collected matched lengths, C1;2 C2;2 CbN=2c;2 and CbN=2c 1;2 CbN=2c 2;2 CN;2 , respectively. Step 3. Apply l1 ; l2, and l3 bits burst error correcting codes to theses three sets, respectively, and also let the check-bit parts of the codes be C1 , C2 , and C3 , respectively. Step 4. Output the compressed data by LZ77 coding and the check-bit parts C1 , C2 , and C3 . Evaluation Figure 10.27 shows relation between the error location in the compressed data and the error recovery capability of the scheme. In this case, C1 , C2 , and C3 are determined by l1 16 bits, l2 12 bits, and l3 8 bits burst error correcting Fire codes, respectively. Because the combined length of the offset and the last symbol is much larger than the total length of the matched length in this model, the burst error correction length l1 takes rather large value. The source le is paper1. The check-bit length is 105 bits for the 238,176 bits of compressed data and 48-bit burst errors are injected. The length of the offset, the matched length, and the length of the last symbol are same as those in Figure 10.25. Note in the comparison of Figure 10.27 the dramatic difference between the case of the 40-bit burst error correcting Fire code with 119 check bits applied to compressed data uniformly and the case of no error control code, denoted as without ECC. Also note that the UEP scheme is the more powerful method to control errors than the existing burst error control code method applied uniformly to the compressed data. The simulations using other source les [BELL90] yielded similar results.
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